An improved mathematical model bidirectional coupling of heat-water and mechanics during vacuum pre-cooling

Vacuum pre-cooling is a multi-physics process coupling heat transfer, water transport, and shrinkage, the stresses caused by water evaporation and temperature variation in food interact with its deformation. However, the developed models usually assume that the shrinkage of food is insignificant so that it is ignored, which is inconsistent with the actual vacuum pre-cooling process and makes the simulation results inaccurate. Taking strawberry as an example, a multiphase porous media model with heat-water and mechanics (HWM) bi-directional coupling was developed for food vacuum pre-cooling. The accuracy of the HWM model was verified by comparing the heat-water (HW) model without considering shrinkage and the experiments. The results show that the development of the evaporation front predicted by the HWM model is more sensitive to the vacuum chamber pressure change compared with the HW model. The maximum average relative errors corresponding to the temperature and shrinkage of the HWM model are 0.27% and 6.95%, respectively, which are better than the HW model. In addition, the edge gradient effect that occurs in the middle stage of vacuum pre-cooling was observed. When the vacuum chamber pressure approached the lowest point, the evaporation region rapidly developed toward the core. The increase of evaporation driving force and the decrease of boundary moisture caused drastic temperature and shrinkage changes on the product surface. The model developed in this paper considering shrinkage provides technical support to optimize the vacuum pre-cooling process and improve product quality. • Shrinkage of strawberry during vacuum pre-cooling was modeled. • Heat and mass transfer model coupled with shrinkage was developed. • An improved method of predicting vacuum chamber pressure was proposed. • The edge gradient effect due to pressure drop was predicted.